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Optimizing Neighborhood-Scale Walkability
Andrew J. Sonta, S.M.ASCE,1 Rishee K. Jain, Ph.D., A.M.ASCE2
1Urban Informatics Lab, Department of Civil & Environmental Engineering, Stanford University,
473 Via Ortega Room 269B, Stanford, CA 94107; e-mail: asonta@stanford.edu
2Urban Informatics Lab, Department of Civil & Environmental Engineering, Stanford University,
473 Via Ortega Room 269A, Stanford, CA 94107; e-mail: rishee.jain@stanford.edu
ABSTRACT
Many designers and researchers have grappled with the problem of optimally locating
buildings and use types in a neighborhood-scale development. But little work has used data-driven
optimization to aid in creating urban design schemes. The paradigm of single-use Euclidian zoning
has heavily impacted the way our neighborhoods, cities, and suburbs are designed, resulting in the
physical separation of uses. However, as we grapple with emerging issues of environmental and
social sustainability in cities, there is a pressing need to consider alternative urban designs that
require less dependence on personal automobiles and that foster healthier cities. In this paper, we
develop a methodology for (1) automatically assessing the walkability of neighborhoods by
adopting a common walkability metric and (2) optimizing the layout of buildings and amenities
across a known grid in order to maximize the walkability metric. We apply this methodology to a
case study of the Potrero Hill neighborhood in San Francisco, California. We find that, in
comparison to the existing layout that can be characterized by Euclidian-style separation of uses,
the optimized layout suggests distributing amenities across the street network, resulting in a two-
fold increase in walkability. This tool and analysis have the potential to provide computational and
data-driven support for urban designers and researchers hoping to understand and improve the
walkability of urban spaces.
INTRODUCTION
The design and planning of urban spaces has a long and storied history, with ideas about the
best use of urban space dating to Ancient Rome. Some of the earliest plans for cities—including
Paris, London, and Washington, D.C.—were created by master-builders or architects with the
NOTICE: This is the authors’ version of a conference manuscript that was accepted for
publication in the Proceedings of the International Conference on Computing in Civil
Engineering 2019 in Atlanta, GA. Changes from the publishing process, such as editing,
corrections, and formatting may not be reflected in this manuscript. A definitive version can
be accessed via the following link: https://doi.org/10.1061/9780784482438.058
Please cite this research as follows:
Sonta, A. J., and Jain, R. K. (2019). Optimizing Neighborhood-Scale Walkability, in
Computing in Civil Engineering 2019: Data, Sensing, and Analytics (Atlanta, GA), pp. 454–
461, American Society of Civil Engineers.
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backing of government. Today, almost all cities implement some form of urban planning vis-à-vis
rules about building form, use, and location (Best 2016).
Single-use zoning, also known as Euclidian zoning—in which cities are divided into areas with
specific rules for building height, use, and density—became possible and prevalent after the
landmark case Village of Euclid v. Amber Realty Co. in 1926 (Wickersham 2000). In the period
following World War II, the physical separation of functional uses in cities became both feasible
and desirable due to increased rates of property ownership and use of the personal automobile
(Best 2016). Even in dense cities, single-use zoning replaced existing mixed-use developments
(Jacobs 1961). However, recent environmental and social concerns (e.g., the public and planetary
health consequences of automobile pollution) have led urbanists, local governments, and city
planners to rethink rigid Euclidian rules. One important reason is that developments with a mix of
uses reduce residents’ dependence on personal vehicles. Aside from the obvious environmental
implications, urbanists such as Jane Jacobs (1961) have argued that increased use of sidewalks and
reduced dependence on cars create vibrant, socially resilient communities. As a result, the study
and desirability of walkable communities have increased greatly in recent years.
Recently, we have also seen a vast surge in urban data resources and computing power. Given
these resources, researchers now have a unique opportunity to put these concepts of ideal urban
form to the test. This dual paradigm of evolving urban planning concepts and maturing cyber-
physical analysis has the potential to validate or entirely upend the consensus of what makes a city
effective. As a result, there is a pressing need to explore how computing tools such as optimization
can augment current decision-making processes around zoning and rule-making in urban areas.
Given the complexity of city planning—which includes street and path layouts, building
geometries, and use types—various approaches must be explored. In this paper, we develop a
methodology for maximizing the walkability of a neighborhood-scale development by choosing
the layout of buildings in an existing street grid, given the number of buildings, each building’s
prescribed use, and possible lots for placing each building. In a case study, we compare the existing
layout of a neighborhood in San Francisco, CA with an optimized layout that distributes key urban
amenities quite differently.
BACKGROUND
Recent urban design research has identified the concept of walkability as a key metric in
addressing environmental and social sustainability concerns in cities. Porta and Renne (2005)
include interconnectedness and accessibility of the street network as a critical component of their
tool for assessing the sustainability of urban form. Furthermore, they argue that in addition to these
street network characteristics, the community must colocate a diversity of land uses so that
multiple uses can be accessed by walking.
Some studies have used heuristic algorithms to optimize the walkability of neighborhood-sized
developments. These heuristics produce best-practice guidelines for walkable communities built
on architectural and urban design expert knowledge (Southworth 2005). While these guidelines
can be important and effective tools for urban designers in their planning work, they lack an
objective score that can be automatically calculated and applied quickly to various design
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alternatives. Exploiting automated computational tools can greatly expand the solution space and
reveal previously overlooked options.
A few recent studies have explored the notion of optimizing physical layouts of structures in
real-world environments. Razavialavi and Abourizk (2017), for example, developed a genetic
algorithm framework for optimizing layout on a construction site. Rakha and Reinhart (2012)
developed a generative modeling platform that assesses different parametric urban massing forms
for walkability. They adopt the walkability scoring system discussed in Carr et al. (2010) as the
metric for optimization, and they utilize a genetic algorithm to optimize walkability by placing
different uses. This previous quantitative optimization work, while valuable in advancing the role
of computing in assessing urban form, has not been applied to evaluate the performance of existing
urban areas. Furthermore, the implications of the walkability optimization results have not been
fully explored, especially in their relationship to conventional wisdom about effective urban
design.
METHODOLOGY
The purpose of the methodology outlined in this section is to maximize a quantitative
walkability metric of a neighborhood-scale development given constraints about the number and
possible locations for each building type. The methods we outline here can be used to compare
optimized layout of buildings and amenities with alternative designs, including those created
through heuristics or those that already exist in cities.
Our approach follows a procedure with three main steps:
1. Problem definition—define the walkability objective function and how it is measured, and
define the solution space (i.e., possible locations of buildings) as well as the constraints
(i.e., number of each building type available).
2. Generate random designs—develop a routine for creating a population of randomly
generated designs, which are defined by the locations of each building type.
3. Optimize design—assess designs, create a new set of designs based on the best performers,
and repeat until convergence.
Problem Definition
In order to accomplish the ultimate goal of maximizing walkability, we first need a walkability
metric and a set of variables that can be changed to vary this metric. In this paper, we adopt the
metric discussed in Rakha and Reinhart (2012) and hereafter refer to it as the Street Score. The
Street Score is a value between 0 and 100, and it is calculated for one residential unit at a time. In
its most general form, the Street Score (
!
) is calculated as the sum of walking distance scores
between each residential unit and a prescribed number of different amenities (e.g., parks,
restaurants, grocery) as follows:
!"#
$
%&
'()*(
+
(,-
.
#//
where the vector
'(
is the weighting vector for amenity
0
and the vector
*(
is the distance score
vector for amenity
0
(defined below). The vectors
'
and
*
can have different sizes for each
amenity, but the size of
'(
is always equal to the size of
*(
. This difference in vector sizes is
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simply a function of the fact that the implementation of the Street Score metric can specify different
numbers of each amenity to consider in the scoring (e.g., 2 coffee shops vs. 20 restaurants). The
distance score is calculated as a function of the walking distance (
1
) from the residential unit to
the amenity under consideration. This walking distance must be defined according to the street
grid (e.g., in a perpendicular north-south, east-west grid, the distance would be the L1 norm, or the
“Manhattan” walking distance). For instance
2
of amenity
0
, the distance score is calculated as
follows:
3(45"
6
#
#78/9:
;
<=7<-
>?
@
;
17<-
>
/9#78/9#
;
<A7<=
>
@
? ;
17<=
>
<BBBBBBBB 1C<-
<-D1C<=
<=D1C<A
1E<A
for walking distance
1
, where
<-
,
<=
, and
<A
are set by the user. The result is a score, based on the
distance, that is scaled between 0 and 1.
The design variables for the problem are the locations of buildings and amenities. The
categories of buildings/amenities can be set according to the individual problem, but it is important
to note that the initial work by Rakha and Reinhart used residential units, restaurants, generic
shops, coffee shops, bookstores, banks, grocery stores, parks, schools, and entertainment venues.
In this initial work, we simplify the design space by defining specific lots at which different
buildings of different sizes can be placed.
Optimization
Given a calculable objective function (Street Score) and design variables (locations of build-
ings/amenities), the next step is to perform optimization. We utilize a genetic algorithm, as these
have been shown in previous work to be effective in optimizing physical layouts with large
solution spaces (Rakha and Reinhart 2012; Razavialavi and Abourizk 2017). Each step in the
genetic algorithm requires creating a routine specific to this specific problem setting. These
subroutines are outlined in this subsection. To initialize the population, we must be able to create
random designs. Given a street grid with possible lots as well as a building stock with numbers of
available building/amenity types, we can randomly assign each building type to a lot. For
implementation, it can be simplest to randomly assign larger amenities—that may take up multiple
lots—first, working from largest amenities to smallest. Once an initial population is created, a
Street Score can be calculated for each neighborhood design. To adapt the Street Score
methodology from a single residential unit to an entire neighborhood, we randomly sample
residential units from a neighborhood, calculate the Street Score for each, and average the results.
Given Street Scores calculated for all neighborhood designs, we can select parents that will help
us create future generations. Different selection criteria can be utilized, including truncation
selection, tournament selection, and roulette wheel selection, as discussed in Kochenderfer (2018).
Once parents are selected, crossover and mutation must be implemented to create new
generations. The process for crossover is detailed in Algorithm 1. The notion is to randomly choose
the location of each building/amenity from the parents’ locations for that building/amenity. First,
all non-residential buildings are selected from the parents and placed, and then the residential units
are filled in randomly. The concept of simulated annealing can be incorporated into the overall
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genetic algorithm through modification of simple crossover (and mutation), as discussed in Adler
(1993). In simulated annealing crossover, a child is created from two parents, and it is always
accepted if it performs better than the parents. If it performs worse than its parents, it is accepted
with a probability that shrinks over generations. Formally, the child is accepted with the following
probability: F
#
BGHIB
J
KLMNOP4#
Q
BBBBR!D/
R!E/
where
R!
is the difference between the child’s Street Score and the best of the parents’ Street
Scores, and
S
is a temperature value that decreases according to an exponential annealing schedule,
which makes use of the following decay factor:
S
;
TU-
>
"VS;T>
, where
V
is a user-defined
parameter.
The algorithm for mutation is shown in Algorithm 2. Mutation is only performed on a child
with probability given as a parameter in the overall genetic algorithm. When it is performed, a
given number of randomly chosen non-residential buildings/amenities are swapped with
residential buildings/amenities. Mutation is implemented in this way because the relative locations
of residential units and non-residential amenities are the key drivers in the Street Score function.
Simulated annealing can also be applied to mutation, using the original individual and the mutated
individual as the candidates for acceptance. Crossover and mutation are used to create new
generations of neighborhood designs. In the overall algorithm, we track the best performing
individuals to determine the overall most walkable neighborhood design.
CASE STUDY: POTRERO HILL, SAN FRANCISCO, CALIFORNIA
To evaluate the proposed optimization methodology and test it on a real-world urban area, we
apply it to an existing neighborhood-scale urban design in the Potrero Hill area of San Francisco,
California. The grid we consider in this case study is 9 blocks by 3 blocks and roughly 320,000 m2
in area. Figure 1 shows the abstracted study space, the amenities that are present in the design
space, and weight vector associated with each amenity (as described above). These amenities are
found and categorized through a manual audit of the space using Google Maps. The categorizations
and weights in this study largely follow those in Rakha and Reinhart’s previous work, which were
chosen based on their analysis of both importance and the need for choice (as lengths of the weight
vectors indicate how many of each amenity are considered in the calculation of the Street Scores).
We increased the weight for the park amenity given its prominence in the existing design.
Furthermore, consistent with Rakha and Reinhart, we did not consider offices to be an amenity.
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To convert the physical layout to an abstract layout with appropriate dimensions and with lots
for placing buildings and amenities, we used the osmnx package (Boeing 2017) for Python. We
made certain assumptions in order to simplify the abstract representation of the neighborhood.
Based on our assessment of the study area, we assume that, on average, there are 32 possible lots
in each block. We also assume that the park and the schools each occupy one full block—where a
full block is defined as the lots entirely contained by four intersections. Furthermore, we assume
that all other building types each occupy one lot. It is important to note that this last assumption
could be easily changed such that different building/amenity types take up different numbers of
lots and/or partial lots to reflect multi-use development. For this study, however, we aimed to keep
the abstract neighborhood representation as simple as possible in order to focus on optimization
and interpretation.
For calculating the Street Score, we need to set values for the parameters
<-
,
<=
, and
<A
(discussed above). Given the geometry of the neighborhood, we set
<-"W/X
,
<="Y//X
, and
<A"#Z//X
. It is important to note that these values are smaller than they are in Rakha and
Reinhart’s initial work. We choose smaller values because the physical distances in our case study
are much smaller than those in the Rakha and Reinhart study, and therefore it would be relatively
difficult to achieve a perfect Street Score. For the existing urban layout, we calculate the Street
Score to be 31.8.
Figure 1. Potrero Hill existing layout with amenities and their weight vectors.
Figure 2. Comparison of implementations with varying degrees of simulated annealing.
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In order to optimize this layout, we execute the genetic algorithm outlined above. The first step
in this algorithm is to generate an initial population. We first generate a random population of
neighborhood designs and assess their Street Scores. The random design routine first chooses
random blocks for placing the park and schools, since these amenities take up full blocks. It then
chooses random lots for placing all other amenities, and finally it fills up the remaining lots with
residential units. After generating a population of 1,000 individuals, we calculate the Street Score
for each. The resulting distribution has a mean of 52.1 and a standard deviation of 3.4.
We implement a version of truncation selection in the genetic algorithm to bias toward the
better performing individuals. We first sort the individuals by decreasing Street Score (since we
are maximizing). We then choose from the best performing individuals, but we also ensure that a
randomly chosen set of the remaining population is incorporated in the selected group in order to
protect against local minima. The mutation and crossover routines are implemented as discussed
in the Methodology section. On a small population, we test three versions of the genetic algorithm,
each with different levels of use of the concept of simulated annealing. In the baseline case, we do
not include simulated annealing, but we test two other cases: one in which simulated annealing is
incorporated into mutation, and another in which simulated annealing is incorporated into both
mutation and crossover. When simulated annealing is incorporated, we use the exponential
annealing schedule with
V"YO[
. The results from this test are shown in Figure 2 (where GA
represents ‘genetic algorithm’ and SA represents ‘simulated annealing’). As we can see, the
genetic algorithm with simulated annealing incorporated into mutation performs the best.
Once deciding that simulated annealing should only be applied to the mutation step, we execute
the genetic algorithm with the following parameters: 1,000 designs points in a single population,
100 generations, 5% probability of mutation, 500 parents, 4 children per parent pair, and initial
annealing temperature of 10. The optimization convergence is shown in Figure 2. The best
performing individual found after all generations are scored has a Street Score of 68.7. This is a
little more than a two-fold increase from the existing layout (which was 31.8) and a roughly 32%
increase over the random layouts. The final optimized layout is shown in Figure 3.
Figure 3. Optimized neighborhood layout.
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DISCUSSION AND CONCLUSIONS
Results of our analysis indicate that the average Street Score for the randomly generated
layouts is significantly higher than the Street Score for the existing neighborhood layout. Perhaps
even more surprising, the existing layout’s score is about 6 standard deviations below the randomly
generated layouts’ mean score. It is important to note here that the existing layout score could start
to approach the random layout score if the parameters
<-
,
<=
, and
<A
are increased. However, this
finding still suggests a significant difference between the random and existing layouts. This is
partially explained by the fact that the existing layout is reminiscent of the planning notion of
Euclidian zoning. In the existing layout, the shop and restaurant uses are generally clustered in the
lower right hand side of the grid. This clustering negatively impacts the Street Scores for any
residential units located relatively far from the cluster (in our case, the houses on the upper left).
Additionally, the grocery amenity in the existing layout is located all the way in the upper left
corner of the grid, having a similar effect on the scores for residential units on the bottom right.
The optimization routine seems to converge around a maximum about 32% higher than the
random layout. This optimized layout (as seen in Figure 3) has a much more dispersed layout of
amenities. Importantly, the park and grocery amenities are located quite centrally in the grid. In
addition, the schools are distributed on the left and the right, and the restaurants and shops tend to
be distributed evenly across the entire grid. This makes intuitive sense: the more distributed
amenities are, the higher chance that all residential units will be proximate to at least one of each
amenity—questioning the benefits of Euclidean zoning for walkability in urban neighborhoods.
The main limitations in this work result from the various assumptions that were involved in
setting some of the scoring parameters, including the distance parameters and the weighting
parameters. Future work should consider which parameter values are most appropriate for different
problem settings. However, while assumptions had to be made, the results still suggest important
differences between the existing Euclidian-style layout and the more mixed layout suggested
through optimization. Another limitation of this work is that the optimization and analysis were
solely focused on an existing neighborhood layout in a real neighborhood. While the optimization
could be easily applied to a neighborhood designed from scratch, a few things would need to be
known before optimization: the street grid, the number of each building/amenity, and the possible
lots for building/amenity placement. Future work should consider the problem of co-optimizing
the street grid and possible locations along with building placement, as this might provide further
insights into the optimal design for the urban fabric.
Finally, the findings from this analysis should not be the sole input when designing a new
layout or assessing the performance of an existing layout. To be sure, there are metrics other than
walkability that should be seriously considered when designing an urban space, such as proximity
of amenities to transit stops, public health effects, or expected economic activity. The relative
colocation of a polluting factory with a grocery store may increase walkability, but it could have
dire consequences for public health. Similarly, it may improve walkability to distribute amenities
across a given area, but for canonical economic reasons such as those first suggested in Hotelling’s
law (Hotelling 1929), it may be more economically profitable for two similar businesses to be
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located near each other. While the work presented in this paper cannot provide a sole rationale for
designing a neighborhood one way versus another, it can provide helpful input for urban designers,
engineers, and city governments in considering new layouts or evaluating existing ones.
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